Find potential outside and inside of a uniformly charge (q) sphere of radius R. Also, plot V as afunction of distance.

To solve this problem, we will use Gauss's law and the definition of electric potential.

Step 1: Gauss's Law Gauss's law states that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity of free space. For a uniformly charged sphere, the electric field is zero inside the sphere and kQ/r^2 outside the sphere (where k is Coulomb's constant, Q is the total charge, and r is the distance from the center of the sphere).

Step 2: Electric Potential The electric potential V at a distance r from a point charge Q is given by V = kQ/r.

Step 3: Potential Inside the Sphere Inside the sphere (r<R), the electric field is zero, so the electric potential is constant and equal to the potential on the surface of the sphere, which is V = kQ/R.

Step 4: Potential Outside the Sphere Outside the sphere (r>R), the potential decreases as 1/r, so V = kQ/r.

Step 5: Plotting V as a Function of Distance To plot V as a function of distance, you would plot V on the y-axis and r on the x-axis. The plot would be a horizontal line at V = kQ/R for r<R, and a hyperbola decreasing as 1/r for r>R. The two parts of the plot meet at r=R.

Note: The potential is continuous at r=R, which means that the potential inside the sphere meets the potential outside the sphere at r=R. This is because the electric field is conservative, which means that the work done by the field in moving a charge from one point to another is independent of the path taken.